Question

You (or your parents) purchase a car for $28,125.00 plus 7.5% sales tax. The down payment is $3,125.00. You have a fair credit rating. What is your new principal balance at the beginning of the second month if you pay $529.75 at the end of the first month?


Secured

Unsecured

Credit

APR (%)

APR (%)

Excellent

3.95

4.57

Good

4.45

5.04

Average

4.90

5.75

Fair

5.60

6.55

Poor

7.05

8.70

(1 point)
Responses

$26,706.14
$26,706.14

$27,595.25
$27,595.25

$29,704.53
$29,704.53

$26,579.63

Answer 1

To determine the new principal balance at the beginning of the second month after making the payment, let's follow these steps:

1. **Calculate the total cost of the car including sales tax**:
\[
\text{Sales tax} = \text{Car Price} \times \text{Sales Tax Rate} = 28,125 \times 0.075 = 2,109.375
\]
\[
\text{Total cost of the car} = \text{Car Price} + \text{Sales tax} = 28,125 + 2,109.375 = 30,234.375
\]

2. **Determine the loan amount after the down payment**:
\[
\text{Loan Amount} = \text{Total cost} - \text{Down Payment} = 30,234.375 - 3,125 = 27,109.375
\]

3. **Calculate the monthly interest rate** based on the APR for fair credit (5.60%):
\[
\text{Monthly Interest Rate} = \frac{\text{APR}}{12} = \frac{5.60\%}{12} = 0.4667\% = 0.004667
\]

4. **Calculate the interest for the first month**:
\[
\text{Interest for first month} = \text{Loan Amount} \times \text{Monthly Interest Rate} = 27,109.375 \times 0.004667 \approx 126.79
\]

5. **Calculate the new principal balance after the first payment**:
\[
\text{New Principal} = \text{Loan Amount} + \text{Interest for first month} - \text{Payment}
\]
\[
\text{New Principal} = 27,109.375 + 126.79 - 529.75 \approx 26,706.14
\]

Thus, the new principal balance at the beginning of the second month is **$26,706.14**.